发布求助
文献互助 智能选刊 最新文献

J. Num. Math.最新文献

筛选
英文 中文
Analysis of the streamline-diffusion finite element method on a piecewise uniform mesh for a convection-diffusion problem with exponential layers 指数层对流扩散问题的分段均匀网格流线扩散有限元分析
J. Num. Math. Pub Date : 1900-01-01 DOI: 10.1515/JNMA.2001.59
M. Stynes, L. Tobiska
{"title":"Analysis of the streamline-diffusion finite element method on a piecewise uniform mesh for a convection-diffusion problem with exponential layers","authors":"M. Stynes, L. Tobiska","doi":"10.1515/JNMA.2001.59","DOIUrl":"https://doi.org/10.1515/JNMA.2001.59","url":null,"abstract":"Abstract On the unit square, we consider a singularly perturbed convection-diffusion boundary value problem whose solution has two exponential boundary layers. We apply the streamline-diffusion finite element method with piecewise bilinear trial functions on a Shishkin mesh of O(N 2) points and show that the error in the discrete space between the computed solution and the interpolant of the true solution is, uniformly in the diffusion parameter ɛ, of order ɛ 1/2 N –1 lnN + N – 3/2 in the usual streamline-diffusion norm. This includes an L 2-norm error estimate of order O(N – 3/2) in the convection–dominated case ɛ ⩽ N – 1 ln–2 N. As a corollary we prove that the method is convergent of order N –1/2 ln3/2 N (again uniformly in ɛ) in the local L ∞ norm on the fine part of the mesh (i.e., inside the boundary layers). This local L ∞ estimate within the layers can be improved to order ɛ 1/2 N –1/2 ln3/2 N+N –1 ln1/2 N, uniformly in ɛ, away from the corner layer.","PeriodicalId":342521,"journal":{"name":"J. Num. Math.","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115209571","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 14
Finite difference approximations for space–time fractional partial differential equation 时空分数阶偏微分方程的有限差分近似
J. Num. Math. Pub Date : 1900-01-01 DOI: 10.1515/JNUM.2009.016
Y. Zhang
{"title":"Finite difference approximations for space–time fractional partial differential equation","authors":"Y. Zhang","doi":"10.1515/JNUM.2009.016","DOIUrl":"https://doi.org/10.1515/JNUM.2009.016","url":null,"abstract":"Abstract An implicit difference scheme is presented for a space–time fractional convection–diffusion equation. The equation is obtained from the classical integer order convection–diffusion equations with fractional order derivatives for both space and time. First-order consistency, unconditional stability, and first-order convergence of the method are proven using a novel shifted version of the classical Grünwald finite difference approximation for the fractional derivatives. A numerical example with known exact solution is also presented, and the behavior of the error is examined to verify the order of convergence.","PeriodicalId":342521,"journal":{"name":"J. Num. Math.","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122323404","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Frontmatter
J. Num. Math. Pub Date : 1900-01-01 DOI: 10.1515/jnma-2020-frontmatter4
{"title":"Frontmatter","authors":"","doi":"10.1515/jnma-2020-frontmatter4","DOIUrl":"https://doi.org/10.1515/jnma-2020-frontmatter4","url":null,"abstract":"","PeriodicalId":342521,"journal":{"name":"J. Num. Math.","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129064682","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Adaptive finite element solution of eigenvalue problems: Balancing of discretization and iteration error 特征值问题的自适应有限元解:离散化与迭代误差的平衡
J. Num. Math. Pub Date : 1900-01-01 DOI: 10.1515/jnum.2010.015
R. Rannacher, A. Westenberger, W. Wollner
{"title":"Adaptive finite element solution of eigenvalue problems: Balancing of discretization and iteration error","authors":"R. Rannacher, A. Westenberger, W. Wollner","doi":"10.1515/jnum.2010.015","DOIUrl":"https://doi.org/10.1515/jnum.2010.015","url":null,"abstract":"Abstract This paper develops a combined a posteriori analysis for the discretization and iteration errors in the solution of elliptic eigenvalue problems by the finite element method. The emphasis is on the iterative solution of the discretized eigenvalue problem by a Krylov-space method. The underlying theoretical framework is that of the Dual Weighted Residual (DWR) method for goal-oriented error estimation. On the basis of computable a posteriori error estimates the algebraic iteration can be adjusted to the discretization within a successive mesh adaptation process. The functionality of the proposed method is demonstrated by numerical examples.","PeriodicalId":342521,"journal":{"name":"J. Num. Math.","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116369737","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 39
Numerical method of lines for evolution functional differential equations 演化泛函微分方程的直线数值方法
J. Num. Math. Pub Date : 1900-01-01 DOI: 10.1515/jnum.2011.004
Z. Kamont, Milena Netka
{"title":"Numerical method of lines for evolution functional differential equations","authors":"Z. Kamont, Milena Netka","doi":"10.1515/jnum.2011.004","DOIUrl":"https://doi.org/10.1515/jnum.2011.004","url":null,"abstract":"Abstract We give a theorem on error estimates of approximate solutions for the ordinary functional differential equation. The error is estimated by a solution of an initial problem for nonlinear differential functional equation. We apply this general result to the investigation of the convergence of the numerical method of lines generated by evolution functional differential equations. Initial boundary value problems for Hamilton Jacobi functional differential equations and parabolic functional differential problems are considered. Nonlinear estimates of the Perron type with respect to the functional variable for given operators are assumed.","PeriodicalId":342521,"journal":{"name":"J. Num. Math.","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125450487","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
Overlapping Schwarz domain decomposition preconditioners for the local discontinuous Galerkin method for elliptic problems 椭圆型问题局部不连续Galerkin方法的重叠Schwarz域分解预条件
J. Num. Math. Pub Date : 1900-01-01 DOI: 10.1515/jnum.2011.008
A. Barker, S. C. Brenner, L. Sung
{"title":"Overlapping Schwarz domain decomposition preconditioners for the local discontinuous Galerkin method for elliptic problems","authors":"A. Barker, S. C. Brenner, L. Sung","doi":"10.1515/jnum.2011.008","DOIUrl":"https://doi.org/10.1515/jnum.2011.008","url":null,"abstract":"Abstract We propose and analyze overlapping two-level additive Schwarz preconditioners for the local discontinuous Galerkin discretization. We prove that the condition number of the preconditioned system is bounded by C[1 + (H/δ)], where H represents the coarse mesh size, δ measures the overlap among the subdomains, and the constant C is independent of H, δ, the fine mesh size h and the number of subdomains Ns . Numerical results are presented showing the scalability of the method.","PeriodicalId":342521,"journal":{"name":"J. Num. Math.","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128938767","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 13
Fictitious domain method to model a movable rigid body in a sound wave 模拟声波中可动刚体的虚拟域方法
J. Num. Math. Pub Date : 1900-01-01 DOI: 10.1515/jnum-2012-0014
David Imbert, S. McNamara
{"title":"Fictitious domain method to model a movable rigid body in a sound wave","authors":"David Imbert, S. McNamara","doi":"10.1515/jnum-2012-0014","DOIUrl":"https://doi.org/10.1515/jnum-2012-0014","url":null,"abstract":"Abstract Motivated by experiments on the acoustics of submerged granular media, we have developed a new fictitious domain method that combines the acoustic wave equation with the equations of motion of a rigid body. The coupling is realized through the natural boundary conditions of the wave equation on the surface of the body and enforced with boundary Lagrange multipliers. The method is validated using analytic solutions for a movable rigid sphere in a sound wave. Results show that the method is promising because numerical results and analytic solutions are close for long wavelengths, although some deviations occur when the wavelength is smaller to the sphere radius. This method permits us to use a discrete element method for particle motion and interaction, and finite elements for wave propagation in the fluid.","PeriodicalId":342521,"journal":{"name":"J. Num. Math.","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130892650","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Localised FE-analysis of Strang's problem based on Lagrange techniques 基于拉格朗日技术的斯特朗问题局部有限元分析
J. Num. Math. Pub Date : 1900-01-01 DOI: 10.1515/jnum.2010.006
F. Suttmeier
{"title":"Localised FE-analysis of Strang's problem based on Lagrange techniques","authors":"F. Suttmeier","doi":"10.1515/jnum.2010.006","DOIUrl":"https://doi.org/10.1515/jnum.2010.006","url":null,"abstract":"Abstract Performing numerical analysis in elastoplasticity, in several situations one observes plastic regions to cause difficulties in deriving nearly optimal error estimates under adequate regularity assumptions. In this note, for a typical model problem we propose an alternative estimate for the discretisation error localised to these critical parts. The discretisation error, measured locally in terms of stresses, is controlled by an a priori interpolation result and an a posteriori consistency estimate. The interpolation part possesses optimal order convergence in terms of the mesh size together with an adequate regularity assumption on the stresses. The consistency part is fully computable and does not contain heuristics.","PeriodicalId":342521,"journal":{"name":"J. Num. Math.","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133695352","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Robust residual a posteriori error estimators for the Reissner–Mindlin eigenvalues system Reissner-Mindlin特征值系统的鲁棒残差后验误差估计
J. Num. Math. Pub Date : 1900-01-01 DOI: 10.1515/jnum-2013-0004
E. Creusé, S. Nicaise, Emmanuel Verhille
{"title":"Robust residual a posteriori error estimators for the Reissner–Mindlin eigenvalues system","authors":"E. Creusé, S. Nicaise, Emmanuel Verhille","doi":"10.1515/jnum-2013-0004","DOIUrl":"https://doi.org/10.1515/jnum-2013-0004","url":null,"abstract":"Abstract We consider a conforming finite element approximation of the Reissner- Mindlin eigenvalue system, for which a robust a posteriori error estimator for the eigenvector and the eigenvalue errors is proposed. For that purpose, we first perform a robust a priori error analysis without strong regularity assumption. Upper and lower bounds are then obtained up to higher order terms that are superconvergent, provided that the eigenvalue is simple. The convergence rate of the proposed estimator is confirmed by a numerical test.","PeriodicalId":342521,"journal":{"name":"J. Num. Math.","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115189663","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
An anisotropic functional setting for convection-diffusion problems 对流扩散问题的各向异性函数设置
J. Num. Math. Pub Date : 1900-01-01 DOI: 10.1515/JNMA.2001.199
C. Canuto, A. Tabacco
{"title":"An anisotropic functional setting for convection-diffusion problems","authors":"C. Canuto, A. Tabacco","doi":"10.1515/JNMA.2001.199","DOIUrl":"https://doi.org/10.1515/JNMA.2001.199","url":null,"abstract":"Abstract A new functional framework for consistently stabilized discrete approximations to convection-diffusion problems was recently proposed. The key ideas are the evaluation of the residual in an inner product of the type H –1/2 and the realization of this inner product via explicitely computable multilevel decompositions of function spaces. Here we improve such approach, by taking into account the anisotropic nature of the convection-diffusion operator. We derive uniform (in the diffusion parameter) anisotropic estimates for both the exact and the discrete solutions and we study the convergence of the approximation. To this end we develop a functional framework involving anisotropic Sobolev spaces which depend on the velocity field.","PeriodicalId":342521,"journal":{"name":"J. Num. Math.","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129153393","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 12
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信